Related papers: Analytical graphic statics
Graph structure learning aims to learn connectivity in a graph from data. It is particularly important for many computer vision related tasks since no explicit graph structure is available for images for most cases. A natural way to…
Procedural models (i.e. symbolic programs that output visual data) are a historically-popular method for representing graphics content: vegetation, buildings, textures, etc. They offer many advantages: interpretable design parameters,…
This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…
The advent of artificial intelligence (AI) technologies has significantly changed many domains, including applied statistics. This review and vision paper explores the evolving role of applied statistics in the AI era, drawing from our…
Our modern life has grown to depend on many and nearly ubiquitous large complex engineering systems. Many disciplines now seemingly ask the same question: ``In the face of assumed disruption, to what degree will these systems continue to…
There has been a recent surge of interest in using machine learning to approximate density functional theory (DFT) in materials science. However, many of the most performant models are evaluated on large databases of computed properties of,…
Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. However, the mathematical reasons for this success remain…
Despite the prevalence of recent success in learning from static graphs, learning from time-evolving graphs remains an open challenge. In this work, we design new, more stringent evaluation procedures for link prediction specific to dynamic…
Graphs have a superior ability to represent relational data, like chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks including comparison,…
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
Dynamic graph neural network (DGNN) is becoming increasingly popular because of its widespread use in capturing dynamic features in the real world. A variety of dynamic graph neural networks designed from algorithmic perspectives have…
Social and information networks are gaining huge popularity recently due to their various applications. Knowledge representation through graphs in the form of nodes and edges should preserve as many characteristics of the original data as…
The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
We simulate static memory materials on a two-dimensional lattice. The bulk properties of such materials depend on boundary conditions. Considerable information can be stored in various local patterns. We observe local probabilities…
Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions.…
Presenting long sequences of dynamic graphs remains challenging due to the underlying large-scale and high-dimensional data. We propose dg2pix, a novel pixel-based visualization technique, to visually explore temporal and structural…
Contrastive learning has become a key component of self-supervised learning approaches for graph-structured data. Despite their success, existing graph contrastive learning methods are incapable of uncertainty quantification for node…
Graph learning models have demonstrated great prowess in learning expressive representations from large-scale graph data in a wide variety of real-world scenarios. As a prevalent strategy for training powerful graph learning models, the…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…